1 Department of Mathematics, Technical University of Denmark2 Operations Research, Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Informatics and Mathematical Modeling, Technical University of Denmark4 Department of Wind Energy, Technical University of Denmark5 Department of Management Engineering, Technical University of Denmark
In this paper we present a hierarchical optimization method for finding feasible true 0-1 solutions to finite element based topology design problems. The topology design problems are initially modeled as non-convex mixed 0-1 programs. The hierarchical optimization method is applied to the problem of minimizing the weight of a structure subject to displacement and local design-dependent stress constraints. The method iteratively solves a sequence of problems of increasing size of the same type as the original problem. The problems are defined on a design mesh which is initially coarse and then successively refined as needed. At each level of design mesh refinement, a neighborhood optimization method is used to solve the problem considered. The non-convex topology design problems are equivalently reformulated as convex all-quadratic mixed 0-1 programs. This reformulation enables the use of methods from global optimization, which have only recently become available, for solving the problems in the sequence. Numerical examples of topology design problems of continuum structures with local stress and displacement constraints are presented.
topology optimization, convex mixed integer programming, local branching, neighborhood search